Hostname: page-component-848d4c4894-8kt4b Total loading time: 0 Render date: 2024-06-27T05:36:01.097Z Has data issue: false hasContentIssue false
  • English
  • Français

The role of negative energy waves in some instabilities of parallel flows

Published online by Cambridge University Press:  19 April 2006

R. A. Cairns
R. A. Cairns
Affiliation:
Department of Applied Mathematics, University of St Andrews, Fife, Scotland
Get access Rights & Permissions [Opens in a new window]

Abstract

Parallel flows with step function velocity and density profiles can support waves which have negative energy, in the sense that exciting them lowers the total energy of the system. A number of instabilities can occur because of the coexistence of positive and negative energy waves, or because of the damping of negative energy waves; some particular examples are discussed to show how appreciation of this role of negative energy waves allows one to predict the existence of instability before doing any detailed analysis, and to gain insight into the instability mechanism.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 92 , Issue 1 , 15 May 1979 , pp. 1 - 14
Copyright
© 1979 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Acheson, D. J. 1976 On over-reflexion. J. Fluid Mech. 77, 433–472Google Scholar
Bekefi, G. 1966 Radiation Processes in Plasmas. Wiley
Benjamin, T. B. 1963 Classification of unstable disturbances in flexible surfaces bounding inviscid flows. J. Fluid Mech. 16, 436–450Google Scholar
Briggs, R. J. 1964 Electron-Stream Interaction with Plasmas. M.I.T. Press
Coppi, B., Rosenbluth, M. N. & Sudan, R. N. 1969 Nonlinear interactions of positive and negative energy modes in rarefied plasmas. Ann. Phys. (New York) 55, 207–247Google Scholar
Craik, A. D. D. 1968 Resonant gravity-wave interactions in a shear flow. J. Fluid Mech. 34, 531–549Google Scholar
Davidson, R. C. 1972 Methods in Nonlinear Plasma Theory. Academic Press
Dougherty, J. P. 1970 Lagrangian methods in plasma dynamics. I. General theory of the averaged Lagrangian. J. Plasma Phys. 4, 761–785Google Scholar
Francis, J. R. D. 1956 Wave motions on a free oil surface. Phil. Mag. (8) 1, 685–688Google Scholar
Lamb, H. 1906 Hydrodynamics, 3rd ed. Cambridge University Press
Landahl, M. T. 1962 On the stability of a laminar incompressible boundary layer over a flexible surface. J. Fluid Mech. 13, 609–632Google Scholar
Miles, J. W. 1959 On the generation of surface waves by shear flows. Part 3. Kelvin-Helmholtz instability. J. Fluid Mech. 6, 583–598Google Scholar
Simmons, W. F. 1969 A variational method for weak resonant-wave interactions. Proc. Roy. Soc. A 309, 551–575Google Scholar
Stix, T. H. 1962 The Theory of Plasma Waves. McGraw-Hill
Sugaya, R., Sugawa, M. & Nomoto, H. 1977 Experimental observation of explosive instability due to a helical electron beam. Phys. Rev. Lett. 39, 27Google Scholar
Taylor, G. I. 1931 Effect of variation in density on the stability of superposed streams of fluid. Proc. Roy. Soc. A 132, 499–523Google Scholar
Weissman, M. A. 1970 Viscous destabilization of the Kelvin-Helmholtz instability. Notes on Summer Study Prog. Geophys. Fluid Dyn. Woods Hole Oceanog. Inst. no. 70–50Google Scholar